I know of 4 time saves. (sorry I cant post videos)

1st is a minor save in the tutorial puzzle. just run to the wall below the ladder and mash jump. you can get a double/wall jump and reach the ladder. if you get is fast enough (it is easy) you save some time not grabbing the letter to jump off of.

2nd: this one is the hardest skip. and saves about 25 seconds. the puzzle is the one with two snap/ span. the intended way is to drop the ladder down, turn on the snap/ span turn it off when it is open then make the jumps. however, with precise jumps you can just make the jumps without the ladder or turning on the switch. it can actually be one cylced. good time save.

3rd]. know as the escape skip. Found by @MaturedSinner . instead of doing the puzzle you can push the "c" to the left to get to the lower level. push it to the left again and keep following it. during the transition from bottom to top, you can jump and make the hero disappear. the just run to the right until the camera zooms in then pause and retry to warp to the next cutscene. good time save.

4th} I call it the sort skip. it is also realatively easy. It is the numbered puzzle where you make sort/order. to make a bridge to get across the gap. you need to also protect yourself from the gun. I use cover. right before the puzzle there is a small cutscene.

how to skip; right before the cut scene starts, jump forward into the letter maker. you can start to make "cover" during the cut scene. use the cover to get to the floating number blocks. with good jumping you can get to the lower right most block. jump off of it to the right as high as you can. you will die. you will respawn on the higher ledge as if the puzzle was completed.

Platform skip. https://www.youtube.com/watch?feature=youtu.be&v=HyTGOhvRrFs

as far as I know those are the time saving tricks. other than that it is just clean platforming and puzzle solving.

trying to get videos of these.

Tut skip. minor save

Snaps skip

Escape skip (found by @MaturedSinner )

Sort Skip

I've found a quite a few minor timesaves myself, here's one

fast OPEN (saves about 5 seconds) If you notice, the word gets tighter when you're pushing it, then relaxes when you release. If you push it right next to the trigger, let go, and jump as it relaxes, it will activate the cutscene without locking you in place, allowing you to skip ahead a little bit. It stops you a little past the gate, don't think there's a way around that.

fast chapter 3 platform, saves about 6 seconds

100% of the time you encounter this platform it will be on the other side. If you die, the platform spawns on your side, but moving away from you. If you look close you'll notice that I get a little horizontal distance before jumping, this is key. If you jump immediately, you will miss it. Afterwards I run across the platform and perform a late jump to just barely make it over the gap. The late jump saves barely any time though so it's entirely optional. Good, easy time save.

splitting hairs here but you can save a tiny amount of time in the very beginning. as just the "O" when you fall. if you hit back right at the last moment, you can fall straight down without hitting the sides.

Fast Fall

found a timesave very similar to the sort skip. It's the section right before sort skip, with the moving platforms. Saves about 7-8 seconds.

I found a new skip! This saves about 12-13 seconds and uses a glitch originally found by https://www.twitch.tv/brutishki . All you have to do is destroy the T and then stand underneath where it spawns. When the T respawns, if you're in the correct position, you'll get stuck briefly and then teleport upwards. During this brief moment of being stuck, begin moving to the left. When you teleport, you'll teleport into the loading zone of the next area. If the ladder on the right disappears, you did it correctly. Fall to your death OR retry, whichever’s faster depending on your platform.

I finally got the ladder zip (I heard kyten call it this and I like it so credit to him for the name). I still don't know if it can be done consistently but I'm definitely willing to try.

Here’s another one to add to the pile. You pick up the O and then walk as close to the gate as you can. Then, jump and drop the O at the same time while moving to the right, so when you hit the ground you can get in between the O and the gate. Pick up the O and do another jump throw to clip through the gate.

I’m not totally sure how much time this saves yet, but if I had to guess I would say around 7-10 seconds

I finally found a way around getting frozen in place at the end of fast open! For some reason sitting letters down while going uphill is very glitchy, and I’ve been looking into finding timesaves that abuse this. This is the first one I found.

Nailing this is all about timing. You want to perform the glitch at the same time you would get frozen in place in the cutscene. All you have to do is pick up the O, walk left until you get stuck on the hill. Wait until the screen zooms out all the way, then jump up the hill. As soon as you land, sit the letter down. Then continue to move left as the ball rolls you downhill. As soon as you reach the bottom, move to the right. If you can move it worked. Then just keep moving right.

It still stops you at the place where the worm busts out, so it only saves you about 4-5 seconds. If you nail fast open but fuck up fast fast open you negate the time saved by both, so it’s a bit risky for only an extra 5 seconds.

Fast Drain! This one saves around 10-15 seconds, and while I found a consistent setup, this one is still a little tricky.

So the first part of the glitch is setting up the T. I grab the T and throw it closer to the ledge. Next, I push it into a very specific spot, which I have a visual cue for.

I try to make a little triangle with the rock in the top right corner of the T, if that make sense. I let go of the T and grab it again because it pushes the T forward a very tiny amount, so I can fine-tune the position. Once the T is set up, I jump over it and grab the ledge behind it. This is easier said then one, as it’s pretty easy to miss the ledge.

Now this is where the magic happens (or not). As you pull yourself up, spam jump and hold right. If the T is positioned correctly, you’ll teleport upwards. As soon as the teleport happens, stop jumping. It’s easy to jump too much and jump off of the rope. Then just swing the D in to place and you’re good to go.